Due: Friday, April 11, 2014 at 5:00 P.M.
Do the following experiment (you may work in groups of two):
On a separate sheet (see the file “helicopter”), a “T” is drawn.
Cut out the “T”, making sure that the body is ½ inch wide and the wings are ½ inch wide. Slit the line in the middle of the wings (without tearing them off).
At the intersection of the body and the wings, bend each wing along the dotted line at a 45 degree angle, one inwards and one outwards, so that the angle between the two wings will be a right angle. (Upon turning the “T” 90 degrees around its body, it should look like a “Y”, with a long body and tiny wings.) In principle, if you raise the “T” to a high enough level and drop it, it will go down encircling itself, like a helicopter.
The goal of this project is to design a “helicopter” that goes down as slowly as possible. Do the following:
1) Raise the helicopter so that its tail is 5 feet above the floor, and let it fall. Using a stopwatch, time how long it takes to reach the floor. Repeat this 5 times.
2) Cut off part of the wings (symmetrically from each side) and/or part of the body. Choose 4 wing lengths and 4 body lengths (such that the helicopter will not drop like a stone). For each of the 16 combinations repeat step #1. You may start with a smaller size “T” than the one distributed (for example, by cutting off some of the body or wing before starting, or by making your own “T”, but be sure that the width of the body and the wings remain ½ inch each). Be sure to note the wing spans and body length for each run of the experiment.
Finally:
1) Analyze your data by a 2-way ANOVA. Is there interaction? What are the main effects (if any)? Which is the best of the 16 combinations? After seeing the data, which of the combinations can be said to be worse than the best one? (Use an overall 5% level of significance.)
2) Analyze your data by multivariate regression. Is the model linear in the body length and in the
wingspan, or are there higher order terms (such as quadratic, etc.)?
3) Do the data give a clue as to what is the best design (wing span and body length that maximize the mean time that the helicopter remains in the air)?
4) What are the differences between the ANOVA and the regression analysis?
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